Open AccessLifts of connections to the bundle of (1,1) type tensor frames
Author(s) -
Habil Fattayev
Publication year - 2021
Publication title -
sigma mühendislik ve fen bilimleri dergisi
Language(s) - English
Resource type - Journals
eISSN - 1304-7191
pISSN - 1304-7205
DOI - 10.14744/sigma.2021.00007
Subject(s) - connection (principal bundle) , bundle , mathematics , geodesic , frame bundle , normal bundle , metric connection , pure mathematics , tensor (intrinsic definition) , parallel transport , vector valued differential form , principal bundle , tensor field , type (biology) , metric tensor , mathematical analysis , topology (electrical circuits) , line bundle , geometry , vector bundle , ricci curvature , combinatorics , fundamental theorem of riemannian geometry , exact solutions in general relativity , curvature , geology , paleontology , materials science , composite material
In this paper we consider the bundle of (1,1) type tensor frames over a smooth manifold, define the horizontal and complete lifts of symmetric linear connection into this bundle. Also we study the properties of the geodesic lines corresponding to the complete lift of the linear connection and investigate the relations between Sasaki metric and lifted connections on the bundle of (1,1) type tensor frames.